Reaction Orders and Kinetics in Biochemistry

Reaction Orders in Chemical Kinetics

Introduction to Reaction Orders

Understanding reaction orders is essential for analyzing how the concentration of reactants affects the rate of a chemical reaction. This concept is foundational in biochemistry, especially when studying enzyme kinetics and metabolic pathways.

• Reaction order: The exponent to which the concentration of a reactant is raised in the rate law. It indicates how the rate depends on the concentration of that reactant.

• For a general reaction: $aA + bB \rightarrow cC + dD$ The rate law is: $\text{Rate} = k[A]^m[B]^n$ where m and n are the reaction orders with respect to A and B, respectively.

• Reaction orders are experimentally determined and do not necessarily match the stoichiometric coefficients except for elementary reactions.

Elementary vs. Non-elementary Reactions

• Elementary reactions: Single-step reactions where the reaction order equals the stoichiometric coefficients of the reactants.

• Non-elementary reactions: Multi-step reactions where the overall reaction order is determined experimentally and may not match the stoichiometry.

Type	Example	Overall Reaction Order
Elementary	2O3(g) → 3O2(g)	Order = 2 (from stoichiometry)
Non-elementary	NO2(g) + CO(g) → NO(g) + CO2(g)	Order = experimentally determined

Types of Reaction Orders

Zero Order Reactions

In zero order reactions, the rate is independent of the concentration of the reactant.

• Rate law: $\text{Rate} = k$

• Units of k: M/s

• Common in enzyme-catalyzed reactions when the enzyme is saturated with substrate.

Example: Decomposition of ammonia on a platinum surface. Graph: Rate vs. [Substrate] is a horizontal line.

First Order Reactions

First order reactions have rates directly proportional to the concentration of one reactant.

• Rate law: $\text{Rate} = k[A]$

• Units of k: s-1

• Common in radioactive decay and many biochemical processes.

Example: Hydrolysis of esters. Graph: Rate increases linearly with [A].

Second Order Reactions

Second order reactions depend on the concentration of two reactants or the square of one reactant.

• Rate law: $\text{Rate} = k[A]^2$ or $\text{Rate} = k[A][B]$

• Units of k: M-1s-1

• Common in bimolecular reactions.

Example: Reaction between NO and O2. Graph: Rate increases quadratically with [A] or linearly with [A] and [B].

Pseudo First Order Reactions

These are reactions that are actually second order but appear first order because one reactant is in large excess and its concentration remains nearly constant.

• Rate law simplifies to first order with respect to the limiting reactant.

Example: Hydrolysis of sucrose in water (water is in large excess).

Determining Reaction Order

• For elementary reactions, reaction order equals the sum of the stoichiometric coefficients of the reactants.

• For non-elementary reactions, reaction order must be determined experimentally.

Practice Problems and Applications

• Given a rate law $v = k[A]^m[B]^n$, the overall reaction order is $m + n$.

• For a reaction $A + B \rightarrow C$, if $\text{Rate} = k[A][B]$, it is second order overall.

• For a reaction $A \rightarrow B$, if $\text{Rate} = k[A]$, it is first order.

Sample Calculation

• Given: $A + B \rightarrow C$, [A] = 20 mM, rate = 5 μM/min, rate law $v = k[A][B]$.

• Calculate k: $k = \frac{\text{rate}}{[A][B]}$ (Assume [B] is also 20 mM if not specified.)

Summary Table: Reaction Orders

Order	Rate Law	Units of k	Graphical Behavior
Zero	$\text{Rate} = k$	M/s	Horizontal line
First	$\text{Rate} = k[A]$	s-1	Straight line
Second	$\text{Rate} = k[A]^2$ or $k[A][B]$	M-1s-1	Parabola or straight line (for two reactants)

Key Takeaways

• Reaction order is crucial for understanding how changes in concentration affect reaction rates.

• Zero, first, and second order reactions have distinct rate laws and units for the rate constant.

• Experimental determination is necessary for non-elementary reactions.

• Pseudo first order reactions simplify kinetic analysis when one reactant is in large excess.

Additional info: Reaction order concepts are foundational for enzyme kinetics (e.g., Michaelis-Menten kinetics), metabolic regulation, and drug metabolism in biochemistry.